A conjectural bound on the second Betti number for hyper-Kähler manifolds

Abstract

In previous work, we noted that the known cases of hyper-Kähler manifolds satisfy a natural condition on the LLV decomposition of the cohomology; informally, the Verbitsky component is the dominant representation in the LLV decomposition. Assuming this condition holds for all hyper-Kähler manifolds, we obtain an upper bound for the second Betti number in terms of the dimension.

9 pages; to appear in Bull. Soc. Math. France. Final version

References in corpus (1)

• The LLV decomposition of hyper-Kaehler cohomology

Cited by in corpus (1)

• The LLV decomposition of hyper-Kaehler cohomology